A surge in the number of women taking part-time jobs has helped employment in Britain to jump by its biggest amount since spring last year in the latest sign that the labour market may be levelling out.

The Office for National Statistics also reported that the labour force survey, which uses the wider International Labour Organisation (ILO) measure of unemployment, rose by its smallest quarterly amount since March to May last year. That measure rose by just 21,000 in the three months to October to 2.49 million. But that was still enough to give a jobless rate of 7.9%, the worst for 13 years.

The ONS said a 122,000 jump in part-time working in the three months to October was entirely driven by women taking those jobs. Full-time employment, by contrast, fell by 69,000 from the previous three months. Statisticians said part of the rise in employment was due to an extra 23,000 jobs being created in the National Health Service in the latest quarter, which pushed up employment in the public sector to 6.1 million – about a fifth of all jobs.

The ONS said the claimant count – which only measures those drawing unemployment benefit – fell by 6,300 in November to 1.63 million and a jobless rate of 5%. October's rise was also revised down by about half to 5,900 – a far cry from the monthly rises of about 100,000 seen earlier in the year.

Economists say a big shift to part-time jobs or cuts in hours has helped prevent unemployment rising as far or as fast as in the recessions of the early 1980s or 1990s or as fast as in the United States, where the jobless rate has doubled to 10%.

But the news was far from uniformly good. The data revealed that the number of 16- to 24-year-olds out of work was 952,000 in the three months to October, a quarterly rise of 6,000 and the highest figure since records began in 1992.

The number of people out of work for more than a year increased by 49,000 in the latest quarter to 620,000, the worst total since 1997.

"Young people are starting work in these jobs – it is making a difference. To see these falls in unemployment at this stage in the recession is a very, very different picture to the one we saw in the 1980s and 90s."

But the shadow work and pensions secretary, Theresa May, said: "This is yet more evidence of the devastating effect the recession is having on young people. We cannot afford to risk losing a generation of people to Gordon Brown's recession.

"Labour makes many claims about tackling the recession yet behind the unemployment figures there are many families struggling to cope where one or both adults have been put on to part-time work."

Vicky Redwood, of Capital Economics, warned that it was too early to sound the all-clear: "The fact that the rise in employment has been driven entirely by part-time workers suggests that firms remain nervous. A second leg downwards in the labour market remains a key risk for 2010."

The TUC general secretary, Brendan Barber, said: "The economy is still on a knife edge. While the overall quarterly figures are encouraging ... it is vital the government continues to dedicate significant resources to tackling joblessness.

"After falling for two successive months, today's rise in youth unemployment is disappointing. The UK is nowhere near the levels reached in the 1980s but the government must continue to invest to prevent a second wave of rising unemployment amongst 16-24-year-olds."

The figures also showed the number of people classed as economically inactive, including those on long-term sickness benefit or who have given up looking for a job, was 7.9 million, down by 1,000 over the three months but up by 96,000 compared with last year. More than one in five working-age people are now economically inactive.